Finite Group DatabasebetaFinite Group Databasebeta| order | 6592 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42 · Schur multiplier (H2) = C2×C4 |
| direct product | C4×#13110088 |
| Fitting | C4×C8×C103 ⋊ C2 |
| Sylow | C103 ⋊ C4×M16 |
| subgroup | G/H | |
|---|---|---|
| center | C42 | C2×D103 |
| commutator | C2×C103 | C2×C42 |
| Frattini | C2×C4 | C22×D103 |
| Fitting | C4×C8×C103 | C2 |
| socle | C22×C103 | C22×C4 |
| hypercenter | C4×C8 | D103 |
| hypocenter | C103 | C4×M16 |
| LCS | G ▷ C2×C103 ▷ C103 | |
| UCS | C1 ◁ C42 ◁ C4×C8 | |
142 conjugacy classes of subgroups.
1672 conjugacy classes. The character table is too large to display.
| maximal subgroup of | C8×#13110088, #27193423, #27193430, … |
| maximal normal subgroup of | C8×#13110088, #27193423, #27193430, … |
| maximal quotient of | C8×#13110088, #27193430, #27193438, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6592, 499);